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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13680.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13680.f1 | 13680q3 | \([0, 0, 0, -4323, 101522]\) | \(11968836484/961875\) | \(718035840000\) | \([2]\) | \(16384\) | \(1.0182\) | |
| 13680.f2 | 13680q2 | \([0, 0, 0, -903, -8602]\) | \(436334416/81225\) | \(15158534400\) | \([2, 2]\) | \(8192\) | \(0.67159\) | |
| 13680.f3 | 13680q1 | \([0, 0, 0, -858, -9673]\) | \(5988775936/285\) | \(3324240\) | \([2]\) | \(4096\) | \(0.32502\) | \(\Gamma_0(N)\)-optimal |
| 13680.f4 | 13680q4 | \([0, 0, 0, 1797, -50182]\) | \(859687196/1954815\) | \(-1459261578240\) | \([2]\) | \(16384\) | \(1.0182\) |
Rank
sage: E.rank()
The elliptic curves in class 13680.f have rank \(1\).
Complex multiplication
The elliptic curves in class 13680.f do not have complex multiplication.Modular form 13680.2.a.f
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
